Unsupervised Kalman filter approach to signature estimation for remotely sensed imagery

The commonly used linear spectral unmixing is generally performed on a single pixel basis and does not take advantage of inter-pixel spatial correlation. The Kalman filter has been considered to extend the linear unmixing by taking into account both spectral and spatial correlation. In addition to a linear mixture model implemented as a measurement equation, it includes a state equation to keep track of changes in between pixels. However, Kalman filtering requires the complete knowledge of image endmembers present in image data, which is generally not available and very difficult to obtain a priori. In order to relax this dilemma, this paper presents an unsupervised Kalman filtering (UKF) approach to signature estimation for remotely sensed images. It first uses an anomaly detector combined with orthogonal subspace projection (OSP) to extract desired image endmember signatures directly from the image data, then further applies a discrimination measure to classify the extracted signatures into a set of distinct signatures that will be used in the measurement equation. In order for the UKF to effectively capture spatial correlation among sample image pixels, the state equation is also implemented dynamically to adjust the state transition matrix adaptively. Experimental results have shown that the proposed UKF approach provides additional advantages over the commonly used spectral-based linear unmixing methods.